When they're over-compressed to accomplish volume, and ignore the dynamic range available to CDs, the sound becomes mushy, and detail becomes lacking. It can turn a nice, dense-sounding mix into a pile of mush that's indistinguishable from the last band you listened to.
Over-compression kills the harmonics and transients of a signal, altering its character significantly. It's one of the reasons so many bands sound like they're all using the same gear.
It can also make an album physically painful to listen to, Morph the Cat and Vapor Trails being prime examples. Ever wonder why it's harder to sit through a whole album these days? Slamming a CD's volume level and removing dynamic range is a major contributing factor.